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What is the most test problems of Numerical Methods in the mid and end of semester at undergraduate level that probably must come out in the test?

I am taking Numerical Methods and Finite Element Method course on this semester.

As I was read here that Numerical Methods for Partial Differential Equation is the fundamental of the Finite Element Method, then I guess I should start to learn numerical methods first from here.

Btw, there are Numerical METHODS & Numerical ANALYSIS and Finite Element METHODS & Finite Element ANALYSIS. ANALYSIS & METHOD, what is the difference?